Opening angles of collapsar jets θj~CxΓ0-1 (C~1/5) Akira MIZUTA Computational Astrophysics Lab. RIKEN Kunihito IOKA KEK SN&GRB 2013 @ YITP Kyoto Univ. 14.11.2013 Reference: MA, Nagataki, Aoi, ApJ, 732, 26 (2011) MA&Ioka ApJ, 777, 162 (2013)(arXiv:13040163) 1

GRB jet : relativistic collimated outflow 105cm 1010cm 1012-13cm 1015-17cm Numerical Hydro Jet propagation (jet structures, opening angle, effect of progenitor structure, photospheric emission etc., i.e., Aloy+00, Zhang, MacFadyen+03,04 Mizuta+06,09,11,13 Morsony+07,10, Lazzati+09,13 Nagakura+11,12, Suzuki+13 …. GRBs are emitted form highly relativistic outflows (Γ>=100). The outflow is believed to be well confined, i.e., jet. At least some long GRBs originate from SN (collapsar model Woosley 93, MacFadyen Woosley99). MIZUTA SN-GRB 2013 @YITP 2

JET: Lj=5.e50 erg/s [0:100s] θ0=10 degrees AM, Nagataki + (2011) JET: Lj=5.e50 erg/s [0:100s] θ0=10 degrees Γ0=5, ε0/c2=80(h0~106) Γ_max~hΓ(>500) r0@1.e9cm Progenitor: 14Msun ,radius=4x1010cm MIZUTA SN-GRB 2013 @YITP 3

Γ Γ Γ Photospheric emission (dissipated photosphere) log10(ρ) log10(ρ) θ0=10degrees 100s injection θ0=10degrees 30s injection log10(ρ) log10(ρ) Γ Γ Bullet free expandion Γ Only dissipated region Γ OA10 [0:100s] OA10 [0:30s] Γ log10(ρ) Γ Γ MIZUTA SN-GRB 2013 @YITP MA+ 2011 , inprep 4

Motivation Numerical simulations show the opening angles of the jet are smaller than the initial opening angle at least for first a few tens of seconds. Complex structure appears. The structure causes variety of photospheric light curves for different viewing angle observers. We examine what determines opening angles from collapsar jets by numerical simulation and analytical way. “Opening angle” measured at a certain radius θ0 Γ final>=2 Γ final>=200 Morsony +07 MIZUTA SN-GRB 2013 @YITP 5

What determines opening angel of jets ? Naive expectation Our model relativistic beaming effect stellar envelopes Γ0 ~θ0 -1 Γ0 ~θ0 -1 Γ0 ~θ0 -1 stellar envelopes Before shock breakout, the jet is influenced by the interaction with stellar envelopes. Before shock breakout , the jet is not well accelerated (Γ~O(10)). Numerical simulations by Zhang et al.,Mizuta et al., Morsony et al. Lazzati et al., Nagakura et al. Analytical work by 　Bromberg et al. (2011) How about the jet evolution after jet breakout ? MIZUTA SN-GRB 2013 @YITP 6

ρ p Γ High resolution hydro. simulations(2D, axisymmetric) High resolution grid points are devoted at least in the jet and a part of cocoon. Δzmin=Δr min=107cm or =5x106cm Ej=5x1050erg/s, r=8x107cm η=h0Γ0=533, Γ0=2.5, 5, 10 Progenitor : Woosley & Heger(2006) M~14Msun, R*=4x1010cm Code: MA+04,06, Riemann solver (Marquina), 2nd order accuracy in space(MUSCL & time(TVD Runge Kutta) progenitor surface p Γ MIZUTA SN-GRB 2013 @YITP Elongated:Aspect ratio is not correct 7

Why is high resolution necessary ? Collimation shock thin layer Γ0=20 Cocoon gas Γ0=10 Γ0=5 θ0=1/Γ0 Bromberg, Levinson (2009) Initial jet size should be small MIZUTA SN-GRB 2013 @YITP 8

Why is high resolution necessary ? hΓ (=const along stream line, steady state :Bernoulli's principle) hΓ is conserved to the reverse shock Along jet axis baryon loading due to numerical diffusion MIZUTA SN-GRB 2013 @YITP 9

Γ0=5 mass density Lorentz factor So many internal oblique shocks have a potential for (Ito's talk on Tuesday day) MIZUTA SN-GRB 2013 @YITP 10

Cocoon confinement (Before jet breakout) pressure Γ0 θ0~1/Γ0 Γ0=5 Γ0=2.5 jet injection After collimation shock, jet is almost cylindrical shape as Bromberg et al. suggested. Some oblique shocks can be seen inside the jet Bromberg + (2011) collimation shock + Cylindrical jet (Γ~Γ0) MIZUTA SN-GRB 2013 @YITP See also Komissarov & Falle 1998 11

Cocoon Light jet and Overpressured Cocoon Begelman & Cioffi (1988) Bromberg +(2011) Given: Lj , ρj , v j, ρa ==> jet dynamics ? Light jet : ρj hjΓ2< ρ ambient ~c Cocoon Energy in the cocoon ~ Lj x t ~ Pc x V c ~ Pc x (vh x t)x (vc x t) Pc can be derived as a function of time MIZUTA SN-GRB 2013 @YITP Momentum balance on rest frame of the head of the jet (Marti+97...) 12

Comparison with analytical model Shock breakout Jet height Conversion position Width of cylindrical jet The results of numerical simulation are good agreement with theoretical model (Bromberg + 2011, see also Komissarov +1997). Since the mass gradient near the stellar surface is so steep, the theoretical model can not be applied. MIZUTA SN-GRB 2013 @YITP 13

Probe particles xnew=xold+vr,zxΔt Every hydro time step probe particles move with the local velocity which is derived hydro calculation, i.e., xnew=xold+vr,zxΔt Probe particles allows us to follow the Lagrangian motion of fluid elements. 32 particles Initial jet nozle Every 0.01s, 32 particles are injected with the jet MIZUTA SN-GRB 2013 @YITP 14

Probe particles cocoon ρ ρ t=2.3s ρ t=4.6s cocoon Before jet breakout the particles which reach the head of the jet move into the cocoon (shocked jet). MIZUTA SN-GRB 2013 @YITP 15

Particle trajectories injected at t=5 s MIZUTA SN-GRB 2013 @YITP 16

Particle trajectories injected at t=5 s Stellar surface Γ -1 Γ -1 Off-center explosion occurs. The location of off- center depends on particle (when and where the particle is injected). MIZUTA SN-GRB 2013 @YITP 17

10s after shock break θj~Γ0-1 x1/5 Time evolution of jet opening angles shock breakout 10s after shock break θj~Γ0-1 x1/5 ~0.08=1/2.5X1/5 ~0.04=1/5X1/5 ~0.02=1/10X1/5 MIZUTA SN-GRB 2013 @YITP 18

θj~Γ0-1 x1/5 θj~Γ0-1 θj~1/5Γ0-1 MIZUTA SN-GRB 2013 @YITP 19

Collimation shock after jet breakout (Pc (z) ∝ z-λ ) Lorentz factor after collimation shock where where λ<2 (to converge the collimation shock) (Komissarov 97) MIZUTA SN-GRB 2013 @YITP 20

p 1D Pressure profile in the cocoon Pc~ r-2 at break Pc~ const Γ~Γ0 acceleration Γ~5xΓ0 Pc~ const Γ~Γ0 Pc~ r-4 after reak Cocoon confinement Off-center pressure profile X Slope is not enough steep (-1.8). Expansion with weak cocoon confinement also works before the free expansion. p MIZUTA SN-GRB 2013 @YITP 21

Distribution of opening angle of GRB jets (t_d>2s)) (t_d<2s)) θj=1/5Γ0<0.2 rad~10grees Constant luminosity and uniform jet can not explain large opening angle jets ==>Structured jet ? Or, long duration (more than a few tens of seconds) activity MIZUTA SN-GRB 2013 @YITP Fong et al. (2012) 22

Summary ●High resolution calculation of jet from collapsars to reduce numerical baryon loading ●Just before and after jet breakout, we observe jet breakout acceleration which leads Lorentz factor about 5xΓ0 . Numerical results and analytical model suggests that both collimation shock and weak confinement work. ●The opening angle after the break for first several seconds θj~CxΓ0-1 (C~1/5) ●Constant luminosity and non-structured jet with a few tens injection can not explain large opening angle jets. Much longer injection or structured jet is necessary. Future works ●3D simulations to see the multidimensional effect (see, Matsumoto's poster) and magnetized jet should be studied. MIZUTA SN-GRB 2013 @YITP 23

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ρ p Γ High resolution case (after shock breakout ) progenitor surface So many oblique shocks progenitor surface p Γ MIZUTA SN-GRB 2013 @YITP 25

Radial mass density profile Model 16TI (Woosley & Heger 2006) 14M_sun, R*~4x1010cm

Relativistic beaming effect GRBs are radiation from relativistic jets (Γ>100)). Fluid rest frame isotropic emission Observer frame Lorentz transformation Γ c Γ (for Φ'=π/2) =1/Γ Angle Φ' in fluid rest fame is transformed to angle Φ. Radiation/ fluid motion concentrates in half opening angle 1/Γ. Relativistic beaming effect can be applied for relativistic isotopic adiabatic expansion. MIZUTA SN-GRB 2013 @YITP 27

Γ0=2.5 mass density Lorentz factor θ0~1/Γ0 is larger than that of Γ0=5.0. As the radius of the jet increases, the momentum flux to push the stellar envelopes drops. MIZUTA SN-GRB 2013 @YITP 28

Opening angle of GRB jets Opening angles of the jet are estimated from the light curve in the afterglow. θj~ several degrees. Opening angles are more than 10 degrees for some GRBs MIZUTA SN-GRB 2013 @YITP Fong et al. (2012) 29